Fixed formatting issues

Author: MohdFuzailHaider

my_script.py

@@ -1,29 +1,30 @@
 import numpy as np
 
+
 class Tableau:
     def __init__(self, tableau):
         self.tableau = tableau
         self.num_rows, self.num_cols = tableau.shape
-    
+
     def pivot(self, row, col):
         # Divide the pivot row by the pivot element
         self.tableau[row] /= self.tableau[row, col]
-        
+
         # Subtract multiples of the pivot row from all other rows
         for i in range(self.num_rows):
             if i != row:
-                self.tableau[i] -= self.tableau[i, col] * self.tableau[row]
+                self.tableau[i] -= (self.tableau[i, col] * self.tableau[row])
 
     def find_pivot_column(self):
-        # The pivot column is the most negative value in the objective row (row 0)
+        # The pivot column is the most negative value in the objective row
         obj_row = self.tableau[0, :-1]
         pivot_col = np.argmin(obj_row)
         if obj_row[pivot_col] >= 0:
             return -1  # No negative value, we are done
         return pivot_col
 
     def find_pivot_row(self, pivot_col):
-        # Calculate the ratios of the right-hand side to the pivot column entries
+        # Calculate the ratio of the righthand side to the pivotcolumnentries
         rhs = self.tableau[1:, -1]
         col = self.tableau[1:, pivot_col]
         ratios = []
@@ -32,7 +33,7 @@ def find_pivot_row(self, pivot_col):
                 ratios.append(rhs[i] / col[i])
             else:
                 ratios.append(np.inf)  # Ignore non-positive entries
-        
+
         pivot_row = np.argmin(ratios) + 1  # Add 1 because we ignored row 0
         if np.isinf(ratios[pivot_row - 1]):
             return -1  # No valid pivot row (unbounded)
@@ -47,7 +48,7 @@ def run_simplex(self):
             pivot_row = self.find_pivot_row(pivot_col)
             if pivot_row == -1:
                 raise ValueError("Linear program is unbounded.")
-            
+
             self.pivot(pivot_row, pivot_col)
 
         return self.extract_solution()
@@ -58,63 +59,66 @@ def extract_solution(self):
             col = self.tableau[i, :-1]
             if np.count_nonzero(col) == 1:
                 solution[np.argmax(col)] = self.tableau[i, -1]
-        return solution, -self.tableau[0, -1]  # Return solution and optimal value
+        return solution, -self.tableau[0, -1]  # Returnsolutionandoptimalvalue
+
 
 def construct_tableau(objective, constraints, rhs):
     """
     Constructs the initial tableau for the simplex algorithm.
-    
+
     Parameters:
     - objective: List of coefficients of the objective function (maximize).
     - constraints: List of lists representing coefficients of the constraints.
     - rhs: List of right-hand-side values of constraints.
-    
+
     Returns:
     - tableau: A numpy array representing the initial simplex tableau.
     """
     n_constraints = len(constraints)
     n_vars = len(objective)
-    
+
     # Creating the tableau matrix
     tableau = np.zeros((n_constraints + 1, n_vars + n_constraints + 1))
-    
+
     # Fill the objective function (row 0, cols 0 to n_vars)
     tableau[0, :n_vars] = -np.array(objective)  # Maximization -> negate
-    
+
     # Fill the constraints
     for i in range(n_constraints):
         tableau[i + 1, :n_vars] = constraints[i]
         tableau[i + 1, n_vars + i] = 1  # Slack variable
         tableau[i + 1, -1] = rhs[i]  # RHS of the constraints
-    
+
     return tableau
 
+
 def solve_linear_program(objective, constraints, rhs):
     # Constructing the tableau
     tableau = construct_tableau(objective, constraints, rhs)
-    
+
     # Instantiate the Tableau class
     simplex_tableau = Tableau(tableau)
-    
+
     # Run the simplex algorithm
     solution, optimal_value = simplex_tableau.run_simplex()
-    
+
     # Output the solution
     print("Optimal Solution:", solution)
     print("Optimal Value:", optimal_value)
 
+
 # Example usage
 if __name__ == "__main__":
     # Coefficients of the objective function: maximize 3x1 + 2x2
     objective = [3, 2]
-    
+
     # Coefficients of the constraints:
     # 2x1 + x2 <= 18
     # x1 + 2x2 <= 20
     constraints = [[2, 1], [1, 2]]
-    
+
     # Right-hand side of the constraints
     rhs = [18, 20]
-    
+
     # Solve the linear program
     solve_linear_program(objective, constraints, rhs)